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Exact minimum number of bits to stabilize a linear system

Kostina, Victoria and Peres, Yuval and Ranade, Gireeja and Sellke, Mark (2018) Exact minimum number of bits to stabilize a linear system. In: 2018 IEEE Conference on Decision and Control (CDC). IEEE , Piscataway, NJ, pp. 453-458. ISBN 978-1-5386-1395-5.

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We consider an unstable scalar linear stochastic system, X_(n + 1) = aX_n + Z_n – U_n.; where a ≥ 1 is the system gain, Z_n's are independent random variables with bounded α-th moments, and U_n'S are the control actions that are chosen by a controller who receives a single element of a finite set {1, …, M} as its only information about system state X_i. We show that M = [a] + 1 is necessary and sufficient for ß- moment stability, for any ß < a. Our achievable scheme is a uniform quantizer of the zoom-in / zoom-out type. We analyze its performance using probabilistic arguments. We prove a matching converse using information-theoretic techniques. Our results generalize to vector systems, to systems with dependent Gaussian noise, and to the scenario in which a small fraction of transmitted messages is lost.

Item Type:Book Section
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URLURL TypeDescription Paper ItemJournal Article
Kostina, Victoria0000-0002-2406-7440
Peres, Yuval0000-0001-5456-6323
Ranade, Gireeja0000-0002-6747-4492
Sellke, Mark0000-0001-9166-8185
Additional Information:© 2018 IEEE. This work was supported in part by the National Science Foundation (NSF) under Grant CCF-1751356, and by the Simons Institute for the Theory of Computing.
Funding AgencyGrant Number
Simons Institute for the Theory of ComputingUNSPECIFIED
Record Number:CaltechAUTHORS:20190204-124407625
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Official Citation:V. Kostina, Y. Peres, G. Ranade and M. Sellke, "Exact minimum number of bits to stabilize a linear system," 2018 IEEE Conference on Decision and Control (CDC), FL, USA, 2018, pp. 453-458. doi: 10.1109/CDC.2018.8619156
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92630
Deposited By: Tony Diaz
Deposited On:04 Feb 2019 20:52
Last Modified:17 Dec 2021 23:08

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